A) \[\pi \,Hz\]
B) \[\frac{1}{\pi }Hz\]
C) \[2\pi \,Hz\]
D) \[\frac{1}{2\pi }Hz\]
Correct Answer: B
Solution :
As here two masses are connected by two springs, this problem is equivalent to the oscillation of a reduced mass \[{{m}_{r}}\] of a spring of effective spring constant. \[T=2\pi \sqrt{\frac{{{m}_{r}}}{{{K}_{eff.}}}}\] Here \[{{m}_{r}}=\frac{{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}=\frac{m}{2}\] Þ \[{{K}_{eff.}}={{K}_{1}}+{{K}_{2}}=2K\] \ \[n=\frac{1}{2\pi }\sqrt{\frac{{{K}_{eff.}}}{{{m}_{r}}}}=\frac{1}{2\pi }\sqrt{\frac{2K}{m}\times 2}\] \[=\frac{1}{\pi }\sqrt{\frac{K}{m}}=\frac{1}{\pi }\sqrt{\frac{0.1}{0.1}}=\frac{1}{\pi }Hz\]
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